please show details in steps and drawing neatly please show details in steps and

Question

please show details in steps and drawing neatly

please show details in steps and drawing neatly The balloon shown below exerts an 800 N force F on the hook at O. The vertical line AB intersects the x -z plane at point A. The angle between the z axis and the line OA is 60degree , and the angle between the line OA and F is 45degree. 3) Express F in terms of Cartesian components; 4) Determine the direction cosines of F; 5) Find the unit vector of F in terms of Cartesian components. Hint: First resolving F into vector components parallel to OA and Oy.

Explanation / Answer

1).

X-component = 800* cos45 *sin60 = 489.9 N

Z-component = 800*cos45 *cos60 = 282.84 N

Y-component = 800 *sin45 = 565.69 N

2).
Direction cosines are = (489.9/800) , (282.84/800), (565.69/800) = 0.6124, 0.3536, 0.7071

3).

unit vector = 0.6124 (i) + 0.3536 (j) + 0.7071 (k)

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